Friday, October 10, 2014

Ebola growing like the penny in the old childhood allowance puzzle

I remember as a child reading the Allowance Puzzle, where one was asked to pick whether it would be better to receive an allowance of a dime in January that would increase by a dime every month for a year or an allowance of a penny that would double every month for a year.
Most children would quickly choose the dime, seeing that \$1.20 was quite a lot of money compared to a penny. And they would be wrong. The child who chose to receive a penny for his January allowance would receive \$20.48 in December to do his Christmas shopping. That is the power of exponential versus arithmetic growth.
It is also the story of the Ebola virus, which has been growing in true exponential form for several weeks now: for every person who dies, two new ones are catching the disease. Most of them will die. The Washington Post has a story entitled "The Ominous Math of the Ebola Epidemic," that is scary reading.
For some reason the "remain calm" crowd keeps telling us that Ebola isn't very contagious. Yet the Spanish nurse who became the first European case believes she contracted the disease when she accidentally or negligently touched her face while taking off her haz-mat suit. This is a description of a disease that is contagious beyond belief. A single touch can result in death.
I don't know what's going to happen. Perhaps some unknown someone from some unknown someplace will do some unknown something to get this thing under control. Eventually (I hope) we are going to have some restrictions on movement to prevent those who know they might have the disease from just hopping a plane to Dallas. Things in the developed world may grind to a halt for a while.
Ebola has an incubation rate of a four to 21 days and often comes on quite mildly; figure a fortnight. So what is the effect of doubling a penny 26 times (in other words a year's theoretical growth of Ebola)? I could figure it out but I'm too lazy, but Dr. Math tells us the result for doubling a penny 30 times. If you double a penny 30 times you'll end up with \$10,737,418.23. Multiply that by 100 to get the number of pennies and you get 1,073,741,823, or roughly the population of Africa.
Of course, the growth rate has to slow at some point; everyone isn't going to die. There is sometimes a tendency for a virus such as this one to act like a young fire consuming tinder in a blaze and then dying down. I think there is a better than even chance the virus will be contained with only a few flare ups that need to be tamped down.
There is also the chance that Africa could see 500 million dead with 500 million addition corpses spread around the rest of the world. And it could be worse. The fact is that nobody can really forecast just how nasty this thing might be, because at its worst it could kill a third of the planet. I don't think it will, but it could. Nobody is going to come out and mention that, except for me. I do think the incredibly slow incubation period of this virus has lulled the public into a false sense of security.
It is in our national interest to devote substantial resources to fighting this disease. As a nation we need to be prepared for disaster, both collectively and individually. I fear that we are not.

1 comment:

Anonymous said...

I agree, we are due for a mass extinction.